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Digital image processing unit 1

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  • 1. www.jntuworld.com LCE/7.5.1/RC 01 TEACHING NOTES Department: ELECTRONICS & COMMUNICATION ENGINEERING Unit: II Date: Topic name: Retarded Potential No. of marks allotted by JNTUK: Books referred: 01. Antennas for All Applications by John D. Kraus & Ronald J. Marhefka 02. Antenna & Wave Propagation by K. D. Prasad 03. www.wikipedia.org Retarded Potential: The retarded potential formulae describe the scalar or vector potential for electromagnetic fields of a time-varying current or charge distribution. The retardation between cause and effect is thereby essential; e.g. the signal takes a finite time, corresponding to the velocity of light, to propagate from the source point r’ of the field to the point r, where an effect is produced or measured. Otherwise, the formulas below correspond to the same superposition principle acting, e.g., in electrostatics for Coulombs law. These are the electromagnetic retarded potentials for an arbitrary source in free space (vacuum). They satisfy the inhomogeneous wave equations for Φ and A in the Lorenz gauge. Here, r is location, t is time, and is the speed of light in a vacuum. tr is the "retarded time"; the time at which light must be emitted from location r’ in order to reach location r at time t. ρ (r,t) is the electric charge density, and J (r,t) is the current density. ε0 is the dielectric constant of free space and μ0 is the magnetic permeability of free space. ф (r,t) is the electrical potential, and A (r,t) is the vector potential. Finally, dτ’ is the integration measure corresponding to r’. From ф (r,t) and A (r,t) the electromagnetic fields E (r,t) and B (r,t) can be calculated, The corresponding advanced potentials, essentially mathematical objects, are: Faculty/Date: HOD/Date: Page 1 of 11
  • 2. www.jntuworld.com LCE/7.5.1/RC 01 TEACHING NOTES Department: ELECTRONICS & COMMUNICATION ENGINEERING Unit: II Date: Topic name: Electric Dipole Radiation No. of marks allotted by JNTUK JNTUK: Books referred: 01. Antennas for All Applications by John D. Kraus & Ronald J. Marhefka 02. Antenna & Wave Propagation by K. D. Prasad 03. www.wikipedia www.wikipedia.org The subscript a stands for advanced, and ta is the "advanced time". Electric Dipole Radiation: In the previous section, we examined the radiation emitted by a short electric dipole of oscillating dipole moment, Where We found that, in the far field, the mean electromagnetic energy flux takes the form. Assuming that the dipole is centered on the origin of our spherical polar coordinate system. ssuming The mean power radiated into the element of solid angle dΩ = sinθdθdψ, centered on the angular ed coordinates (θ,ψ ), is Hence, the differential power radiated into this element of solid angle is simply This formula completely specifies the radiation pattern of an oscillating electric dipole (provided that the dipole is much shorter in length than the wave length of the emitted radiation Of wave-length radiation). course, the power radiated into a given element of solid angle is independent of dP/dΩ; otherwise energy would not be conserved. Finally, the total radiated power is the integral of ove overall solid angles. Dipole Antenna: The dipole antenna or dipole aerial is one of the most important and also one of the most widely used types of antenna. It can be used on its own, or there are many other types of antenna that use the dipole as the basic element within the antenna. Faculty/Date: HOD/Date: Page 2 of 11
  • 3. www.jntuworld.com LCE/7.5.1/RC 01 TEACHING NOTES Department: ELECTRONICS & COMMUNICATION ENGINEERING Unit: II Date: Topic name: Dipole Antenna - 1 No. of marks allotted by JNTUK: Books referred: 01. Antennas for All Applications by John D. Kraus & Ronald J. Marhefka 02. Antenna & Wave Propagation by K. D. Prasad 03. www.wikipedia.org The basic construction of a dipole is quite straightforward - a simple dipole antenna can be constructed from a few simple pieces of wire. In this way antennas including FM dipole antennas, or antennas for the short wave bands can easily be made. These antennas, while not having the performance of other more complicated types of antenna can nevertheless prove very effective and quite satisfactory in many applications. Basic Dipole Facts: The name dipole means two poles and the antenna does in fact consist of two "poles" or sections. These are normally equal in length, making the antenna what is termed a centre fed antenna. Sometimes a dipole may not be fed in the centre, although this is not normally done in most antenna designs. The power is applied to the dipole antenna itself through a feeder. Conversely if the dipole antenna is used for receiving, the received signals are taken away to the receiver through a feeder. The feeder serves to transfer the power to or from the antenna with as little loss as possible. The most common form of dipole has an electrical length of half a wavelength. As a result this antenna is called a half wave dipole. As before the lengths of the wires are both the same. As the total length of the dipole is a half wavelength, this makes each section or leg of the dipole a quarter wavelength long. Faculty/Date: HOD/Date: Page 3 of 11
  • 4. www.jntuworld.com LCE/7.5.1/RC 01 TEACHING NOTES Department: ELECTRONICS & COMMUNICATION ENGINEERING Unit: II Date: Topic name: Dipole Antenna - 2 No. of marks allotted by JNTUK: Books referred: 01. Antennas for All Applications by John D. Kraus & Ronald J. Marhefka 02. Antenna & Wave Propagation by K. D. Prasad 03. www.wikipedia.org Current and Voltage on a Dipole: In order that power flows into or out of an antenna that is transmitting or receiving, there must be associated currents and voltages. The levels of current and voltage vary along the length of the antenna, and it is found that the current distribution along a dipole is roughly sinusoidal. It falls to zero at the end and is at a maximum in the middle. Conversely the voltage is low at the middle and rises to a maximum at the ends. It is generally fed at the centre, at the point where the current is at a maximum and the voltage a minimum. This provides a low impedance feed point which is convenient to handle. High voltage feed points are far less convenient and more difficult to use. When multiple half wavelength dipoles are used, they are similarly normally fed in the centre. Here again the voltage is at a minimum and the current at a maximum. Theoretically any of the current maximum nodes could be used. Dipole Feed Impedance: All antennas have what is termed a feed impedance. This is the impedance that is seen at the point in the antenna where the feeder is connected. The impedance is measured in ohms, and to ensure that the maximum amount of power is transferred between the feeder and the antenna, it is necessary to ensure that the antenna and feeder impedances are matched, i.e. they have the same value. The feed impedance of a dipole antenna is dependent upon a variety of factors including the length, the feed position, the environment and the like. A half wave centre fed dipole antenna in free space has an impedance 73.13 ohms making it ideal to feed with 75 ohm feeder. The feed impedance of a dipole can be changed by a variety of factors, the proximity of other objects having a marked effect. The ground has a major effect. If the dipole antenna forms the radiating element for a more complicated antenna, then elements of the antenna will have an effect. Often the effect is to lower the impedance, and when used in some antennas the feed impedance of the dipole element may fall to ten ohms or less, and methods need to be used to ensure a good match is maintained with the feeder. One method is to use the folded dipole, outlined later on this page. Faculty/Date: HOD/Date: Page 4 of 11
  • 5. www.jntuworld.com LCE/7.5.1/RC 01 TEACHING NOTES Department: ELECTRONICS & COMMUNICATION ENGINEERING Unit: II Date: Topic name: Dipole Antenna - 3 No. of marks allotted by JNTUK: Books referred: 01. Antennas for All Applications by John D. Kraus & Ronald J. Marhefka 02. Antenna & Wave Propagation by K. D. Prasad 03. www.wikipedia.org Polar Diagram: The polar diagram of a half wave dipole antenna that the direction of maximum sensitivity or radiation is at right angles to the axis of the antenna. The radiation falls to zero along the axis of the antenna as might be expected. If the length of the dipole antenna is changed then the radiation pattern is altered. As the length of the antenna is extended it can be seen that the familiar figure of eight pattern changes to give main lobes and a few side lobes. The main lobes move progressively towards the axis of the antenna as the length increases. Dipole Antenna Length: The length of a dipole is the main determining factor for the operating frequency of the dipole antenna. Although the antenna may be an electrical half wavelength, or multiple of half wavelengths, it is not exactly the same length as the wavelength for a signal travelling in free space. There are a number of reasons for this and it means that an antenna will be slightly shorter than the length calculated for a wave travelling in free space. For a half wave dipole the length for a wave travelling in free space is calculated and this is multiplied by a factor "A". Typically it is between 0.96 and 0.98 and is mainly dependent upon the ratio of the length of the antenna to the thickness of the wire or tube used as the element. Its value can be approximated from the graph: Faculty/Date: HOD/Date: Page 5 of 11
  • 6. www.jntuworld.com LCE/7.5.1/RC 01 TEACHING NOTES Department: ELECTRONICS & COMMUNICATION ENGINEERING Unit: II Date: Topic name: Dipole Antenna - 4 No. of marks allotted by JNTUK: Books referred: 01. Antennas for All Applications by John D. Kraus & Ronald J. Marhefka 02. Antenna & Wave Propagation by K. D. Prasad 03. www.wikipedia.org Multiplication factor "A" used for calculating the length of a dipole In order to calculate the length of a half wave dipole the simple formulae given below can be used: Length (metres) = 150 x A / frequency in MHz Length (inches) = 5905 x A / frequency in MHz Using these formulae it is possible to calculate the length of a half wave dipole. Even though calculated lengths are normally quite repeatable it is always best to make any prototype antenna slightly longer than the calculations might indicate. This needs to be done because changes in the thickness of wire being used etc may alter the length slightly and it is better to make it slightly too long than too short so that it can be trimmed so that it resonates on the right frequency. It is best to trim the antenna length in small steps because the wire or tube cannot be replaced very easily once it has been removed. Folded Dipole Antenna: The standard dipole is widely used in its basic form. However under a number of circumstances a modification of the basic dipole, known as a folded dipole provides a number of advantages that can be used to advantage. This type of antenna is often used in the simple FM dipole antennas that can be bought to use as temporary FM broadcast antennas. They are also used within other larger antennas such as the Yagi. In its basic form a dipole consists of a single wire or conductor cut in the middle to accommodate the feeder. It is found that the feed impedance is altered by the proximity of other objects, especially other parasitic elements that may be used in other forms of antenna. This can cause problems with matching and because resistance losses in the antenna system can start to become significant. Additionally many antennas have to be able to operate over large bandwidths and a standard dipole may be unable to fulfil this requirement adequately. Faculty/Date: HOD/Date: Page 6 of 11
  • 7. www.jntuworld.com LCE/7.5.1/RC 01 TEACHING NOTES Department: ELECTRONICS & COMMUNICATION ENGINEERING Unit: II Date: Topic name: Dipole Antenna – 5 & Radiation Resistance No. of marks allotted by JNTUK: Books referred: 01. Antennas for All Applications by John D. Kraus & Ronald J. Marhefka 02. Antenna & Wave Propagation by K. D. Prasad 03. www.wikipedia.org A variation of the dipole, known as a folded dipole provides a solution to these problems, offering a wider bandwidth and a considerable increase in feed impedance. The folded dipole is formed by taking a standard dipole and then taking a second conductor and joining the two ends. In this way a complete loop is made as shown. If the conductors in the main dipole and the second or "fold" conductor are the same diameter, then it is found that there is a fourfold increase in the feed impedance. In free space, this gives a feed impedance of around 300 ohms. Additionally the antenna has a wider bandwidth. In a standard dipole the currents flowing along the conductors are in phase and as a result there is no cancellation of the fields and radiation occurs. When the second conductor is added this can be considered as an extension to the standard dipole with the ends folded back to meet each other. As a result the currents in the new section flow in the same direction as those in the original dipole. The currents along both the half-waves are therefore in phase and the antenna will radiate with the same radiation patterns etc as a simple half-wave dipole. The impedance increase can be deduced from the fact that the power supplied to a folded dipole is evenly shared between the two sections which make up the antenna. This means that when compared to a standard dipole the current in each conductor is reduced to a half. As the same power is applied, the impedance has to be raised by a factor of four to retain balance in the equation Watts = I^2 x R. Radiation Resistance: Radiation resistance is that part of an antennas feedpoint resistance that is caused by the radiation of electromagnetic waves from the antenna. The radiation resistance is determined by the geometry of the antenna, not by the materials of which it is made. It can be viewed as the equivalent resistance to a resistor in the same circuit. Radiation resistance is caused by the radiation reaction of the conduction electrons in the antenna. When electrons are accelerated, as occurs when an AC electrical field is impressed on an antenna, they will radiate electromagnetic waves. These waves carry energy that is taken from the electrons. The loss of energy of the electrons appears as an effective resistance to the movement of the electrons, analogous to the ohmic resistance caused by scattering of the electrons in the crystal lattice of the metallic conductor. While the energy lost by ohmic resistance is converted to heat, the energy lost by radiation resistance is converted to electromagnetic radiation. Power is calculated as, P = I2R Faculty/Date: HOD/Date: Page 7 of 11
  • 8. www.jntuworld.com LCE/7.5.1/RC 01 TEACHING NOTES Department: ELECTRONICS & COMMUNICATION ENGINEERING Unit: II Date: Topic name: Antenna Theorems – 1 No. of marks allotted by JNTUK: Books referred: 01. Antennas for All Applications by John D. Kraus & Ronald J. Marhefka 02. Antenna & Wave Propagation by K. D. Prasad 03. www.wikipedia.org Where I is the electric current flowing into the feeds of the antenna and P is the power in the resulting electromagnetic field. The result is that there is a virtual, effective resistance: This effective resistance is called the radiation resistance. Thus the radiation resistance of an antenna is a good indicator of the strength of the electromagnetic field radiated by a transmitting antenna or being received by a receiving antenna, since its value is directly proportional to the power of the field. Antenna Theorems: Antenna Reciprocity Theorem: In classical treatises on electromagnetic fields and antennas, the antenna theorem is usually formulated as follows: Given two antennas A and B placed at some distance, each of them can be operated either as a transmitting antenna or as a receiving antenna. Suppose that antenna B is kept intact, while the performance of antenna A as a transmitter is modified so that, for a fixed amount of input power, the signal received by antenna B changes by a factor F. Then the same modification changes also the performance of antenna A as a receiver and does so by the same factor F. The theorem follows from certain symmetries of Maxwell equations and its validity is easily verified experimentally. Adaption to Magnetic Resonance: In magnetic resonance the signal is normally detected using what at first sight appears as an induction coil (NMR, MRI) or a resonant cavity (ESR). However, this description presents conceptual problems since classical induction cannot account for the evidently quantum character of MR spectra which implies absorption and emission events involving discrete electromagnetic quanta. Especially in the case of nuclear magnetic resonance (NMR) and imaging (MRI), where one uses induction coils and there is no detectable radiation exiting/entering the sample area, the quantum nature of the phenomenon is not easy to reconcile with classical Faraday induction. Fortunately, it is clear that the interaction energy E between a magnetic moment m of a particle and a magnetic field B is described by the same formula (E = - m.B) in both the classical and the quantum formalism. Consequently, it is this term which plays a key role in resolving the apparent impasse. Since the way how this works out is too long to follow here, let us see right away the result for the radiation-less case of transmitter/receiver coils. The modified theorem, which we might also call the MR reciprocity law, applies to all devices capable of both producing magnetic fields and detecting MR signals. Faculty/Date: HOD/Date: Page 8 of 11
  • 9. www.jntuworld.com LCE/7.5.1/RC 01 TEACHING NOTES Department: ELECTRONICS & COMMUNICATION ENGINEERING Unit: II Date: Topic name: Antenna Theorems - 2 No. of marks allotted by JNTUK: Books referred: 01. Antennas for All Applications by John D. Kraus & Ronald J. Marhefka 02. Antenna & Wave Propagation by K. D. Prasad 03. www.wikipedia.org The sensitivity of a magnetic resonance assembly, used as a receiver, to nuclides present at a point X is proportional to that assemblys efficiency, when used as a transmitter, to generate at that same location X a radiofrequency field B1. The efficiency of the assembly is measured by the amplitude of B1 produced using a fixed input power P. More precisely, what matters is the component of B1 which is transversal to the main field B0, but the orthogonality of B1 and B0 should be guaranteed by the geometry of the design. One great merit of the theorem is that it makes superfluous the old and irrational concept of coil filling factor. Consider, for example, a simple loop like the one in Figure-1 and suppose that we use it as a transmitter to generate an RF magnetic field at point X. When the coil is tuned and matched so that the whole assembly has a predefined impedance Z0 (usually 50 Ω), a fixed power P implies a fixed current J. Suppose now that we reduce the diameter of the loop by a factor F and retune it again to Z0. Then, at input power P, we have still the same current J but, according to the Biot-Savart law, the generated magnetic field B1 is greater than before by the factor F. Consequently, according to the Theorem, the sensitivity of the smaller coil to a nuclide present at X will be F times that of the larger coil. The sensitivity of a front-end assembly at a point X is proportional to the RF field it generates therein when used as a transmitter and fed a pre-defined power. For the test, the input impedance and the current must be kept constant and the assembly must be tuned to the Larmor frequency of the observed nuclides. As always, B1 must be perpendicular to the main magnetic field B0. The above discussion makes sense since it relates the sensitivity of an assembly (inclusive of its tuning and matching circuitry) at a point X to its capability to produce at X a magnetic field when used as an RF field generator rather than a sensor. This combines geometric and electric characteristics of the assembly with the relative location of X - all features which clearly need to be taken into account when talking, for example, about sensitivity to small voxels inside a large MRI coil (notice that in such cases the concept of a filling factor is not applicable at all). It can be shown that the sensitivity to nuclides present at a point X is proportional to, Where B1(X) is the RF field produced at X when the assembly is used as a transmitter and fed the power P. One important and easy to remember corollary of the theorem is the relation between sensitivity and the width of 90o excitation pulse. Since the latter is inversely proportional to the B1 magnitude, it follows that: If a modification of the front-end assembly shortens by a factor F the duration of the 90- degrees pulse, with no change in the employed RF power, the sensitivity of that assembly increases by the same factor F. Faculty/Date: HOD/Date: Page 9 of 11
  • 10. www.jntuworld.com LCE/7.5.1/RC 01 TEACHING NOTES Department: ELECTRONICS & COMMUNICATION ENGINEERING Unit: II Date: Topic name: Loop Antennas - 1 No. of marks allotted by JNTUK: Books referred: 01. Antennas for All Applications by John D. Kraus & Ronald J. Marhefka 02. Antenna & Wave Propagation by K. D. Prasad 03. www.wikipedia.org Loop Antennas: A loop antenna has a continuous conducting path leading from one conductor of a two-wire transmission line to the other conductor. All planar loops are directional antennas with a sharp null, and have a radiation pattern similar to the dipole antenna with E and H fields interchanged. Small Loops: A loop is considered a small loop if it is less than 1/4 of a wavelength in circumference. Most directional receiving loops are about 1/10 of a wavelength. The small loop is also called the magnetic loop because it is more sensitive to the magnetic component of the electromagnetic wave. As such, it is less sensitive to near field electric noise when properly shielded. The received voltage of a small loop can be greatly increased by bringing the loop into resonance with a tuning capacitor. From considerations of symmetry, equal voltages will be induced in each limb of the loop when a signal arrives along the loop axis. The loop output, which is the difference between the limb voltages, is therefore zero in all cases. For signals arriving in the plane of the loop, there is a phase difference between the limb voltages and this produces a maximum output for the small loop. Medium Loops: There are two special cases of loop antennas which are neither short nor long, and have particular characteristics: Half-wavelength loop, a half-wave dipole curved into a circle, can be mounted in the horizontal plane as a horizontally polarized omnidirectional antenna. Full-wavelength loop, an element of the quad antenna, which radiates on its axis (unusual for a loop) and is polarized according to the position of the feed point. Faculty/Date: HOD/Date: Page 10 of 11
  • 11. www.jntuworld.com LCE/7.5.1/RC 01 TEACHING NOTES Department: ELECTRONICS & COMMUNICATION ENGINEERING Unit: II Date: Topic name: Loop Antennas - 2 No. of marks allotted by JNTUK: Books referred: 01. Antennas for All Applications by John D. Kraus & Ronald J. Marhefka 02. Antenna & Wave Propagation by K. D. Prasad 03. www.wikipedia.org Large Loops: The large loop antenna is similar to a dipole, except that the ends of the dipole are connected to form a circle, triangle (delta loop antenna) or square. Typically such a loop is some multiple of a half or full wavelength in circumference. A circular large loop gets higher gain (about 10%) than the other forms, as gain of this antenna is directly proportional to the area enclosed by the loop, but circles of flexible wire can be difficult to support, making squares and triangles much more popular. Large loop antennas are less susceptible to localized noise, partly due to their lack of a need for a ground plane. The large loop usually has its strongest signal in the plane of the loop unless it is very large. The nulls are in the axis perpendicular to the plane of the loop. Faculty/Date: HOD/Date: Page 11 of 11

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